Kim Jong Un boasted on Wednesday that North Korea enters the new year on a surge of strength because of the elimination of ‘‘factionalist filth’’ — a reference to the young leader’s once powerful uncle, whose execution last month raised questions about Kim’s grip on power.

Kim’s comments in an annual New Year’s Day message, which included a call for improved ties with Seoul but also a warning of a possible ‘‘nuclear catastrophe,’’ will be scrutinised by outside analysts and governments for clues about the opaque country’s intentions and policy goals.

Already widespread worry about the country has deepened since Kim publicly humiliated and then executed his uncle and mentor, one of the biggest political developments in Pyongyang in years, and certainly since Kim took power two years ago after the death of his father, Kim Jong Il.

North Korea’s ‘‘resolute’’ action to ‘‘eliminate factionalist filth’’ within the ruling Workers’ Party has bolstered the country’s unity ‘‘by 100 times,’’ Kim said in a speech broadcast by state TV. He didn’t mention by name his uncle, Jang Song Thaek, long considered the country’s No. 2 power.

But Kim included rhetoric that some analysts saw as a first step to renewing dialogue with rival Seoul. Kim called for an improvement in strained ties with South Korea, saying it’s time for each side to stop slandering the other and urging Seoul to listen to voices calling for Korean unification.

That language, which is similar to that of past New Year’s messages, is an obvious improvement on last year’s threats of nuclear war, though there is still skepticism in Washington and Seoul about Pyongyang’s intentions.

North Korea’s authoritarian, secretive government is extremely difficult for outsiders to interpret, and analysts are divided about the meaning of Jang’s execution on treason charges. Many, however, believe that the purge shows Kim Jong Un struggling to establish the same absolute power that his father and grandfather enjoyed.

The public announcement of Jang’s fall opened up a rare and unfavourable window on the country’s inner workings, showing an alleged power struggle between Kim and his uncle after the 2011 death of Kim Jong Il.

Jang’s public downfall was seen as an acknowledgement of dissension and loss of control by the ruling Kim dynasty. That has caused outside alarm as Kim Jong Un simultaneously tries to revive a moribund economy and pushes development of nuclear-armed missiles.

Seoul worries that instability could lead to provocations meant to help consolidate internal unity. Attacks blamed on North Korea killed 50 South Koreans in 2010, and tension on the Korean Peninsula still lingers, although Pyongyang has backed away from war rhetoric from early last year that included threats of nuclear attacks against Washington and Seoul.

Recent indications that North Korea is restarting a mothballed reactor that can produce plutonium for bombs has left Washington and Seoul skeptical about Pyongyang’s recent calls for a resumption of long-stalled nuclear disarmament talks. The country conducted its third nuclear test in February. It’s estimated to have a handful of crude nuclear devices and to be working toward building a warhead small enough to mount on a long-range missile, although most experts say that goal may take years to achieve.

Lim Eul Chul, a North Korea expert at South Korea’s Kyungnam University, said there was a stronger push in this year’s message for improved ties with Seoul, but that doesn’t mean North Korea will take any dramatic steps anytime soon.

Observers say Kim’s vow to improve his people’s living standards could be linked to the comments on better inter-Korean ties, which are seen as necessary to winning badly needed investment and aid.

Robert Carlin, a North Korea expert and contributor to the 38 North website, said Kim’s speech suggests more concrete North Korean proposals are coming. ‘‘Many times over the past 30 or 40 years, the two sides have started dialogue by agreeing to stop slander of the other,’’ Carlin said in an email. ‘‘It’s a relatively easy (and verifiable) first step.’’

In comments that mirror past North Korean propaganda, Kim also warned of an accidental conflict that could trigger ‘‘an enormous nuclear catastrophe,’’ which would threaten U.S. safety.

The 1950-53 Korean War ended with an armistice, not a peace treaty, leaving the peninsula technically in a state of war. About 28,500 American troops are deployed in South Korea to help deter North Korean aggression.